Unit 10 Reflection & Refraction

Transcription

1 Name: Hr: Unit 0 Relection & Reraction Grading: Show all work, keeping it neat and organized. Show equations used and include all units. REFLECTION Vocabulary Relection: The bouncing o light. The angle a beam o light makes when it strikes a surace is described with respect to the normal, an imaginary line drawn perpendicular to the surace. When light shines onto a mirror, the angle at which the light enters the mirror (angle o incidence) is exactly equal to the angle at which the light leaves the mirror (angle o relection). This is called the law o relection and is easily observed in a plane (lat) mirror. Due to the curvature o a spherical or parabolic mirror, light relected rom its surace behaves somewhat dierently than it does when relected rom a plane mirror. There are two types o spherical mirrors: concave (or converging) and convex (or diverging). Concave Convex The ollowing terminology is used when describing how light is relected rom concave and convex mirrors. Vocabulary Object distance: The distance rom the mirror to the object. This value is always a positive number. Vocabulary Image distance: The distance rom the mirror to the image. An image can be real (able to be projected on a screen), or virtual (not able to be projected on a screen). Vocabulary Focal point: The point where parallel rays meet (or appear to meet) ater relecting rom a mirror. The distance rom this ocal point to the mirror is called the ocal length. The ocal length o a concave mirror always has a positive value while the ocal length o a convex mirror always has a negative value. Vocabulary Mirror Equation: = + ocal length object distance image distance = d o + d i Note: Many situations involving mirrors can also be solved using ray diagrams. CONCAVE (CONVERGING) MIRRORS I an object is located more than one ocal length rom a concave mirror as shown in igure A, the image it orms is real, inverted, and in ront o the mirror. You can actually project this image onto a piece o paper. Both d o and d i have positive values. I the object is at the ocal point as in igure B, no image is ormed because the relected rays are parallel.

2 I an object is located less than one ocal length rom a concave mirror as in igure C, the image it orms is virtual, upright, enlarged, and behind the mirror. In other words, you must look into the mirror to see the image. Here, d o has a positive value and d i has a negative value. Figure A Figure B Figure C CONVEX (DIVERGING) MIRRORS The image ormed by a convex mirror is always virtual, upright, smaller, and behind the mirror. The image can be seen only by looking into the mirror. Here d o has a positive value while d i has a negative value. Solved Examples Example : Sitting in her parlor one night, Gerty sees the relection o her cat, Whiskers, in the living room window. I the image o Whiskers makes an angle o 40 with the normal, at what angle does Gerty see him relected? Solution: Because the angle o incidence equals the angle o relection, Gerty must see her cat relected at an angle o 40. Example 2: Wendy, a ortune teller, is polishing her crystal ball. It is so shiny that she can see her relection when she gazes into it rom a distance o 5 cm. a) What is the ocal length o Wendy s crystal ball i she can see her relection 4.0 cm behind the surace o the crystal ball? b) Is this image real or virtual? a) Given: d o = 5 cm d i = -4.0 cm Unknown: =? Original Equation: Solve: = + d o d i = + = d o d i + 5 cm -4.0 cm Getting a common denominator o 60 cm gives = cm 60 cm = - 60 cm To ind, take the reciprocal o this sum. = -60 cm = -5.5 cm. The minus sign beore the answer means that this is the ocal length o a convex mirror. b) The image seen behind a curved surace is always a virtual image.

3 Example 3: With his ace 6.0 cm rom his empty water bowl, Spot sees his relection 2 cm behind the bowl and jumps back. a) What is the ocal length o the bowl? b) What was surprising about Spots s relection that may have caused him to jump? a) Given: d o = 6 cm d i = -2.0 cm Unknown: =? Original Equation: Solve: = + d o d i = + = d o d i + 6 cm -2 cm Getting a common denominator o 2 cm gives = 2-2 cm 2 cm = 2 cm To ind, take the reciprocal o this sum. = 2 cm. The positive answer means that the bowl was acting as a concave mirror. b) The surprising thing Spot noticed about his relection was that it appeared larger than lie! REFRACTION Vocabulary Reraction: The change in direction o light due to a change in speed as it passes rom one medium to another. The path o light is described with respect to the normal. I light is slowed down as it enters a new medium, it bends toward the normal. I it speeds up, it bends away rom the normal. The amount o bending is represented with the letter n, which stands or the index o reraction. The index o reraction or a particular medium is a ratio o the speed o light in a vacuum to the speed o light in the medium. index o reraction = speed o light in a vacuum speed o light in another medium or n = c v Because light travels astest in a vacuum, the index o reraction or any other medium is always greater than. Although the index o reraction or air is.0003, in this chapter the value will be written simply as.00. The angle to which light will bend upon passing rom one medium to another depends upon the index o reraction o each o the two media, n and n 2, and the light s angle o incidence. n sin = n 2 sin 2 This equation is known as Snell s Law. The symbols and 2 stand or the angle o incidence and the angle o reraction, respectively.

4 A special case o this equation is used when light travels rom a more-dense medium to a less-dense medium and the reracted ray makes an angle o 90.0 with the normal as it skims along the boundary o the two media. When this happens, the incident angle is called the critical angle, c. n sin c = n 2 sin 90.0 This is the condition or total internal relection. I the incident angle is any bigger than the critical angle, there is no reraction. Instead, all the light is relected back inside the object. This is called total internal relection. Example 4: Hickory, a watchmaker, is interested in an old timepiece that s been brought in or a cleaning. I light travels at.90 x 0 8 m/s in the crystal, what is the crystal s index o reraction? Given: c = 3.00 x 0 8 m/s v =.90 x 0 8 m/s Unknown: n =? Original Equation: n = c v Solve: n = c = 3.00 x 08 m/s v.90 x 0 8 m/s The index o reraction has no units because it is just a ratio o the speed o light in two dierent media. Example 5: While ishing out on the lake on summer aternoon, Amy spots a large trout just below the surace o the water at an angle o 60.0 to the vertical, and she tries to scoop it out o the water with her net. a) Draw the ish where Amy sees it. b) At what angle should Amy aim or the ish (n water =.33). a) The ish will appear to be straight ahead according to Amy. However, because light travels slower in water than in air, the ish is closer to Amy (and deeper in the water) than she thinks. b) Given: n =.33 (water) n 2 =.00 (air) 2 = 60.0 Unknown: 2 =? Original Equation: n sin = n 2 sin 2 Solve: sin = n 2 sin θ 2 n = (.00) sin (60.0 ).33 = sin - (0.65) = 40.6 = 0.65 Example 6: Binoculars contain prisms inside that relect light entering at an angle larger than the critical angle. I the index o reraction o a glass prism is.58, what is the critical angle or light entering the prism? Given: n =.58 (glass) n 2 =.00 (air) Unknown: c =? Original Equation: n sin c = n 2 sin 90 o Solve: sin c = n 2 sin θ 2 n = (.00) sin (90.0 ).58 = sin - (0.633) = 39.3 = 0.633

5 Exercises Draw a sketch or each exercise! Exercise : Ivan is in a house o mirrors with one o his riends when he comes to two mirrors situated at an angle o 90. Ivan stands so that light shining on his ace is incident on one mirror at an angle o 50, as shown. At what angle will this light relect rom the second mirror? Draw the rays on the diagram, and explain your reasoning below. Exercise 2: A popular lawn ornament in the 960s was a colored relecting sphere that sat in the yard as a decoration. a) I a bird is 0.0 cm rom a blue relecting sphere and sees its image relected 5.0 cm behind the sphere, what is the ocal length o the spherical relector? b) Would the bird s image appear larger or smaller than the bird itsel?

6 Exercise 3: Polly applies her mascara while looking in a concave mirror whose ocal length is 8 cm. She looks into it rom a distance o 2 cm. a) How ar is Polly s image rom the mirror? b) Does it matter whether or not Polly s ace is closer or arther than one ocal length? Explain. Exercise 4: A riend is wearing a pair o mirrored sunglasses whose convex surace has a ocal length o 20.0 cm. I your ace is 40.0 cm rom the sunglasses, how ar behind the sunglasses is your image?

7 Exercise 5: Alison sees a coin at the bottom o her swimming pool at an angle o 40.0 to the normal and she dives in to retrieve it. However, Alison doesn t like to open her eyes in the water so she must rely on her initial observation o the coin made in the air. At what angle does the light rom the coin travel as it moves toward the surace? (n water =.33) Exercise 6: Here s an interesting trick to try. Place a penny in the bottom o a cup and stand so that the penny is just out o sight, as shown. Then pour water into the cup. Without moving, you will suddenly see the penny magically appear. I you look into the cup at an angle o 70.0 to the normal, at what angle to the normal must the penny be located in order or it to just appear in the bottom o the cup? (n water =.33)

8 Exercise 7: Fletcher makes his girlriend a romantic candlelight dinner and tops it o with a dessert o gelatin illed with blueberries. I a blueberry that appears at an angle o 44.0 to the normal in air is really located at 30.0 to the normal in the gelatin, what is the index o reraction o the gelatin? Exercise 8: A jeweler must decide whether the stone in Mrs. Smigelski s ring is a real diamond or a less-precious zircon. He measures the critical angle o the gem and inds that it is 3.3. Is the stone really a diamond or just a good imitation? (n diamond = 2.4, n zircon =.92)